类域

Quadratic algebraic function fields are studied here.Fundamental units forseveral types of such fields are determined explicitly.

本文研究了二次代数函数域，明显决定了几类实二次函数域的基本单位，决定了多类二次函数域的理想类数的下界，给出了类。。。

Prime ideal decomposition is an important problem in algebraic number theory and is relative closely with the class field theory and so on.

素理想分解问题是代数数论中的一个重要课题，它与类域论的关系极为密切，因而如何判断K的素理想在K的有限扩张中的分解状况是一个十分有意义的问题。

In this note, we prove a congruence relation on real quadratic fields which relates class number and certain character sum.

本文证明了关于实二次域的类数和某类特征和的同余式，同时给出某类实二次域的类数可除性的一个判别法则。

In this paper, new classes of linear block codes over finite fields of the algebraicinteger ring of quadratic number fields Qd~(1/2 modulo irreducible elements with norm p or p~2 are presented. These codes can correct one error which takes from the cyclic subgroup of the multiplicative group of the finite fields. The results presented in this paper extend the corresponding results of previous papers.

在处理适用于二维信号的线性分组码时，我们考虑类数为1的有理数域二次扩域Qd~(1/2的代数整数环，利用范数为p或p~2的不可约元构造有限域，给出剩余类域的一组完全陪集代表元系，从而构造出一类有限域上的线性分组码，当错误取值于有限域乘法群的一个循环子群时，所得到的适用于二维信号的线性分组码可以纠单个错，推广了文[14-16]的结果。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

It was the first time the sequence stratigraphy study had been done all across Naimanqi Depression. Jiufotang Formation of Naimanqi Depression was divided into two third-class sequences (SQ1 and SQ2) and five system tracts (SQ1 has LST, TST and HST; SQ2 has TST and HST), and in High System Tract of SQ2, two fourth-class sequences were defined (Ssq1 and Ssq2).2. According to the analysis of core and logging data, we considered that it is the delta fan facies and established the electrofacies model.3. The distribution of reservoir sand bodies had been predicted in the areas without well data by combining the methods of sequence stratigraphy and reservoir inversion. In addition, we summarized the method and process of combining geology and geophysics to predict reservoirs and we made a good prediction by applying it.4. Combining with sequence and depositional types, sandstone thicknesses and reservoir properties, based on Petrel Software platform, we used fuzzy mathematics to comprehensively evaluate reservoirs and define favorable areas. We classified the reservoirs in Naimanqi Depression into five types (TypeⅠ, TypeⅡ, TypeⅢ, TypeⅣand TypeⅤ) and pointed out four favorable areas: Block Nai 1, Block of western Naican 1-Zhangjia Depression, Block Nai 6 and Block of Xinfa-Zhangjia Depression.

其主要创新点如下：1、首次在整个奈曼旗凹陷范围内进行了层序地层学的研究，将奈曼旗凹陷九佛堂组地层分为2个三级层序(SQ1和SQ2)和5个体系域(SQ1由LST、TST和HST组成，SQ2由TST和HST组成)，并在SQ2的高位体系域中又识别出两个四级层序(Ssq1和Ssq2)。2、根据岩芯分析和测井资料识别，定义了研究区扇三角洲沉积相类型，并建立了测井相模板。3、通过层序地层学的研究，结合储层反演，对奈曼旗凹陷层序格架内没有井的区域进行了储层砂体的空间展布预测，并总结了地质-地球物理综合储层预测的方法与思路流程，在应用中取得了良好的预测效果。4、结合层序、沉积类型、砂岩厚度和储层物性等方面，以Petrel软件为基础平台，利用模糊数学的方法进行储层综合评价及有利区划分，将奈曼旗凹陷储层划分为五个级别(Ⅰ类、Ⅱ类、Ⅲ类、Ⅳ类和Ⅴ类)，并预测了四个有利区块，分别为：奈1区块、奈参1西-张家洼子区块、奈6区块和新发-张家洼子区块

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ)，这两类序列具有&优&的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

Automatic color transfer effectively solves this issue. Carve up Roseau and subtractive clustering is applied in this paper. Completely automatic algorithm implementation is realized. In clustering, pixels are selected according to their brightness, and those with larger data density are cluster to sample block. First of colors in the same block are transferred first, others are transferred later.

本文将网格划分减法聚类应用到颜色迁移中，完全实现算法的自动化，聚类方法按照亮度值的大小依次聚类，从各个聚类域中提取出数据点密度较大的像素点集组成样本块，首先对每个样本块间进行颜色迁移，再完成样本块以外的其他像素的颜色迁移。

Which of the following IP addresses fall into the CIDR block of 115.64.4.0/22?

下面的 ip 地址中，哪些属于 115.64.4.0/22 的无类域间路由块？

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。